A spotter is usually used for squeezing out one or two assisted repetitions at the end of a set. The two main benefits are the additional eccentric training and the focus on the target muscle.
A spotter should only assist on the concentric portion of a lift. The eccentric portion of the lift is easier and the body can handle it much better. You can check out our interview with Jazmine Fenlator for a video example of how spotters can be used for eccentric lifts.
The second benefit of using a spotter is the possibility to continue to train a target muscle even if a supporting muscle gives in. Most people rack their bench presses when extending the arms becomes difficult. The shoulders or triceps might be fatiqued and there's a risk that the set could end embarrasingly with the barbell resting on the chest. By using a spotter, you can continue your set by doing a couple of additional half-range bench presses with bended arms to really drain the pecs. The spotter will then assist to rack the barbell.
Personally, I believe 1RM attempts are more dangerous than useful. If using a spotter urges you to attempt one rep maxes, then you might as well train alone. Use a spotter instead to push your body past your mental limits on longer sets.
A spotter should not be confused with a training partner. A spotter is mainly there for your safety. I prefer that the spotter actually has his hands on the barbell at all times, because the failure will happen suddenly. A training partner can sit courtside and cheer his hart out. But not the spotter.